few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Extend the counting sequence.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

Work with numbers 11–19 to gain foundations for place value.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Use place value understanding and properties of operations to add and subtract.

Understand the place value system.

Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Understand place value.

Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 3 of the How Close center which was introduced in grade 1. In this stage, each student picks 7 cards and chooses 4 of them to create 2 two-digit numbers. Each student adds the numbers and the student whose sum is closest to 100 wins a point for the round. It is recommended that at this point in the year, students begin with a target number of 50 instead of 100 in this stage.
If students are not yet able to make 2 numbers that get close to 50, encourage them to choose 2 cards, make a 2 digit number and represent the number with cubes. Then determine how many more cubes they need to get to 50 and choose the 2 cards that will get closest to that number.
Representation: Internalize Comprehension.
Begin by asking, “Do you remember the game, ‘How Close?’” Invite students to recall strategies that helped them work within 20. Ask them to think about how the game will change when the target is 50.
Supports accessibility for: Memory, Attention, Organization
Required Materials
Materials to Gather
Number cards 0–10
Materials to Copy
How Close? Stage 3 Recording Sheet
Launch
Groups of 2
Give one set of digit cards to each group.
“Today we are going to play another game of How Close. This time we will play Close to 50.”
Display the digit cards at the top of the student page.
“We start with 7 cards again. Think about what cards you would choose to make 2 two-digit numbers that have a sum close to 50.”
1 minute: quiet think time
2-3 minutes: partner work time
Share responses.
“After you make your two-digit numbers, you will write an equation showing the sum.”
Demonstrate writing an equation on the recording sheet.
“Now, we see whose sum is closer to 50. Talk to your partner about how you could figure it out.” (You can count up or back from 50 and see whose number is closer.)
30 seconds: quiet think time
1 minute: partner discussion
“Then you will replace the cards you used and play again.”
Activity
"Now play How Close with your partner."
10 minutes: partner work time
Student Facing
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Activity Synthesis
Display digit cards from the student page.
“Diego made the number 38. What number could Diego make next to get close to 50?”


correct_option_index: 4